What is the correct equation to solve for X?

Anna [14]

Answer:

16

Step-by-step explanation:

We can see that Ar is the perpendicular bisector of chord BD. Since A is the center of the circle, AR is the radius of the circle, which is 10 (6+4)

Next, we can see that when we connect point A to point D, it is also a radius. Thus, AD is also equal to 10 as the radius of the circle remains the same.

Using Pythagoras theorem, a^2 + b^2 = c^2, we can make a right angled triangle of ACD.

AC = 6 = a

CD = ? = b

AD = 10 = c

10^2 = 6^2 + b^2

b^2 = 10^2 - 6^2 = 64

b = CD = 8

Now, since Ar is the perpendicular bisector of chord BD, BD = CD x 2

BD = 8 x 2 = 16

5 0

1 year ago

A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m high

Agata [3.3K]

Answer:

dy/dt = 1.02 m/s

Step-by-step explanation:

First of all, let the distance of the dock above the bow of the boat be represented by x.

Also, let the distance of the boat from the dock be represented by y.

Let z represent the length of the rope.

Now, we can use pythagoras theorem to find a relationship between x, y and z since they form a right angle triangle where the vertical part is the dock, the base represents the water and the hypotenuse represents the rope.

Thus;

x² + y² = z²

Using implicit differentiation, we have;

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

We are given that the dock is 1 meter above the bow. Thus, x = 1

Also, the height is not changing and so dx/dt = 0

We are told the dock is 5 feet away from the boat. Thus, y = 5

dy/dt is is the speed we are looking for which is the rate at which the boat is approaching the dock.

We are not given the value of z but we can find it by using pythagoras theorem since we know the dock is 1 meter above the bow and the boat is 5 m away.

Thus;

z = √(1² + 5²)

z = √26

We are told the rope is being pulled in at the rate of 1 m/s. Thus; dz/dt = 1

Plugging all relevant values into the differentiation equation above gives;

2(1)(0) + 2(5)(dy/dt) = 2(√26)(1)

10(dy/dt) = 2√26

Divide both sides by 10 to get:

dy/dt = (√26)/5

dy/dt = 1.02 m/s

5 0

3 years ago

5. Which step is included in the construction of inscribed polygons? (5 points)

RideAnS [48]

Answer:

Your answer is D

Step-by-step explanation:

Your welcome

5 0

3 years ago

On the grid, sketch a graph to represent

Greeley [361]

Answer:

Please find attached, the required graph created on MS Excel

Step-by-step explanation:

The distance between Sandy's house and the school = 200 m

The number of minutes Sandy talked to her friend for = 10 minutes

The time it took Sandy to return home to pick her homework = 5 minutes

Let x represent Sandy's location she stops to talk to her friend 10 minutes, we have;

The slope of the motion on the graph, m₁ = (x - 0)/(t - 0)

The slope of her motion running home to pick the up her homework, m₂ = (x - 0)/(5 - 0)

Given that t > 5, the slope on trip back home, m₁, is larger than are her initial slope, m₂

Therefore, where x = 125, we have;

The rate at which she returned home = m₂ = (125 m - 0)/(5 min - 0) = 25 m/min

Given that the same rate m₂ is what she used in heading back to school, we have;

The time it takes her to get to school = 200 m/(25 m/min) = 8 minutes

Therefore, whereby it took her 10 minutes to reach point x, we have the following coordinate points on the graph in a tabular form;

$\begin{array}{ccc} Time \ (minutes) \ x-axis&&Distance \ (meters) \ y-axis\\0&&0\\10&&25\\15&&0\\23&&200\end{array}$

The plot of the above point is completed using MS Excel as shown in the attached diagram.

7 0

2 years ago

Tell the kind of symmetry this figure has: point, line, plane. (Select all that apply.)

e-lub [12.9K]

Since a circle is simple it has no points but it can be folded many times so symmetry is really unlimited for the circle.It is not a plane because it is round and does not have sides.

5 0

3 years ago

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What is the correct equation to solve for X?￼

What is the correct equation to solve for X?